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A capacitor is constructed from two square metal plates of side length L and sep

ID: 2026805 • Letter: A

Question

A capacitor is constructed from two square metal plates of side length L and separated by a distance d (Figure 6.23). One half of the space between the plates (top to bottom) is filled with polystyrene (k=2.56), and the other half is filled with neoprene rubber (k=6.7). Calculate the capacitance of the device, taking L=2cm and d=0.75mm. (Hint: The capacitor can be considered as two capacitors connected in parallel.)



A capacitor is constructed from two square metal plates of side length L and separated by a distance d (Figure 6.23). One half of the space between the plates (top to bottom) is filled with polystyrene (k=2.56), and the other half is filled with neoprene rubber (k=6.7). Calculate the capacitance of the device, taking L=2cm and d=0.75mm. (Hint: The capacitor can be considered as two capacitors connected in parallel.)

Explanation / Answer

Solution: side lenght of the plates , L=2 cm(10-2 m/1 cm)                                             =0.02 m   Let, the area of the each square plate, A = (Ld) / 2 side lenght of the plates , L=2 cm(10-2 m/1 cm)                                             =0.02 m                                                                   =(0.02 m)(0.75x10-3 m)/2                                                                   =0.0075 x10-3 m2           distance between the plates, d= 0.75 mm(10-3 m/1mm)                                                          =0.75x10-3 m                                di-electric constant of polystyrene (k 1=2.56) fills in the upper half of the capacitor di-electric constant of polystyrene (k 2=6.70) fills in the bottom half of the capacitor permitivity of the free- space (or) air medium is,o =8.54x10-12 Nm2/C2   let, capacitence of the capacitor in upper half of the capacitence be C1    capacitence of the capacitor in upper half of the capacitence be C2                                                 C be the resultant capacitence of C1 and C2    _____________________________________________________________________                                      but ,capacitence of the parallel plate capacitor                                 C =K A o /d   ( General formula) since, these capacitences considered to connect in parallel Resultant capacitnce of these,                        C = C1 + C2                             = k1 Ao / d   + k2 Ao / d                             = [Ao / d ](K1 +K2 )                             = [(0.0075 x10-3 m2)(8.54x10-12 Nm2/C2)/(0.75x10-3 m)](2.56+6.70)                             = 0.0480375x10-12 (9.26) F                             = 0.4448x10-12 F                           (or)                             = 0.448 pF                                                                                 = k1 Ao / d   + k2 Ao / d                             = [Ao / d ](K1 +K2 )                             = [(0.0075 x10-3 m2)(8.54x10-12 Nm2/C2)/(0.75x10-3 m)](2.56+6.70)                             = 0.0480375x10-12 (9.26) F                             = 0.4448x10-12 F                           (or)                             = 0.448 pF                           (or)                             = 0.448 pF